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All digits of the prime 2 x 10³⁰²⁰ - 1 are 9 except 1. It contains 3021 digits. [Williams]

The sum of the first 9 consecutive prime numbers = 10², a perfect square.

If odd Perfect numbers exist, they are of the forms 12n + 1 ... or 36n + 9. [Touchard]

9 is the smallest April Fool prime.

For every prime p with p not equal to 2 and p not equal to 5, there is some number with all digits equal to 9 such that p divides evenly into this number.

Goldbach conjectured that every odd integer greater than or equal to 9 can be represented as the sum of three odd primes.

There are no consecutive-digit primes starting with 9 with digits in descending order. [Madachy]

Define a certain number of irregularly marked points, n, along the rim of a paper circle, then cut along straight lines that join all possible pairs of points. If n = 9, a prime number of separate pieces will be created. 163 to be exact!

The smallest odd Giuga number must have at least 9 prime factors.

If a is greater than b, and b is greater than or equal to 1, then aⁿ + bⁿ has a primitive prime factor with the exception of 2³ + 1³ = 9.

9 times the 9th prime has a sum of digits equal to 9.

There are exactly 9 two-digit emirps. [Croll]

There are no clusters (groups) of 9 Twin prime pairs less than 10¹⁴. [DeVries]

Washington University in St. Louis provides a page that calculates the prime factors of a number (with a maximum of 9 digits).

There are at least 9 prime numbers between x³ and (x + 1)³ for x greater than or equal to , assuming the Riemann Hypothesis is true.

The smallest odd Composite number. [Gupta]

10⁹ + 9 is prime. [Gupta]

Two raised to the 9th power plus and minus 9 are primes! [Hoefakker]

The first digit to appear as an end-digit in two consecutive primes (139 and 149). [Silva]

19, 109, 1009 and 10009 are primes. No other digit can replace the 9 and yield four primes. [Friend]

The number of known positive integers which are the sum of two primes in exactly two ways is a prime square. [Capelle]

2^^n-9 = 2^(2^(2^(....(2^2)...)))-9 is (for large enough n) always divisible by both 7 and 11. Note that 9 is midway between 7 and 11. [Hartley]

The are exactly 3=(sqrt(9)) pandigital improper fractions that reduce to 9 (provided each digit is used once). [Patterson]

100000^9 - 9 and 100000^9 + 9 are primes. Note that 9 is the only known number with this property. [Firoozbakht]

9 is the only number m such that m = ((m)!). [Firoozbakht]

The 9th Fibonacci number plus 9 is prime. [Losnak]